Good Statistical Graphics

Statistical Graphics Literature

History of Graph Criticism:

• KW Haemer, The American Statistician
  “Double Scales are Dangerous” (1948)
  “The Pseudo Third Dimension” (1951)
  “Presentation Problems: Color in Chart Presentation”(1950)

Examples of Good Graphics:

• Naomi Robbins (Creating More Effective Graphs)
• Howard Wainer (Graphic Discovery)

Guidelines for Creating Good Graphs:

• Edward Tufte (The Visual Display of Quantitative Information)

Statistical Graphics Literature

User Studies and Experiments:

• Cleveland & McGill
  

  Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods. (1984)
  Additional Papers in 1985, 1987

• Heer & Bostock (2010) Crowdsourcing graphical perception: using mechanical turk to assess visualization design
• InfoVis: Task specific formal studies of interface design
• Statistical Lineups: Evaluating graphics using a hypothesis-testing framework

  Buja et al. (2009) Statistical inference for exploratory data analysis and model diagnostics
  Hofmann et al. (2012) Graphical Tests for the Power of Competing Designs
  Majumder et al. (2013) Validation of Visual Statistical Inference, Applied to Linear Models

Dissertation

• Data Distortion:
  Perceptual illusions that distort statistical charts
• Signs of the Sine Illusion: Why We Need to Care (JCGS, 2015)
• The Curse of Three Dimensions: Why Your Brain is Lying To You (ASA Student Paper Award, 2014)
• Visual Inference: Exploring the link between statistical graphics and visual ability
• Perception of Multiple Data Features:
  

  How the mapping between data and graphical features affects the hierarchy of graphical perception and feature recognition.

Which Plot has Homogeneous Variance?

4

Which Plot has Homogeneous Variance?

Sine Illusion

Sine Illusion - Explained

Perception is optimized for three dimensions.
Our brains sometimes inappropriately apply 3d heuristics to 2d images, producing optical illusions.

Sine Illusion

Solution 1: Transform X

From: Signs of the Sine Illusion: Why we need to care (JCGS, 2015)

\((f \circ T)(x) = a + (b-a)\left(\int_{a}^x |f^\prime(z)| dz\right)/\left(\int_{a}^{b}|f^\prime(z)| dz\right)\) \((f \circ T_w)(x) = (1-w) \cdot x + w \cdot (f \circ T)(x)\)

Solution 2: Transform Y

From: Signs of the Sine Illusion: Why we need to care (JCGS, 2015)

\(l_{new}(x_0) = l_{old} \sqrt{1 + f^\prime(x_0)^2}\) \(l_{new_w}(x) = (1-w) \cdot l_{old} + w \cdot l_{new}(x)\)

Experimental Validation

Corrections validated experimentally Amazon Mechanical Turk 206 participants completed 1374 trials in 4 days Goals: Identify range of acceptable weight values Examine whether weight values are specific to individuals or consistent within the population

Results

Findings

• Sine Illusion affects our perceptions of statistical graphics
  
  
• Corrections are effective at removing the illusion’s effects
  
  
• Partial correction still is effective
  
  
• “Don’t distort the data”: We need to be concerned with psychological distortion

Outline

Big Data

Visualization is an important tool for working with big data

Adaptations must be made:

• Overplotting (large \(n\))
• High-dimensional data (large \(p\))
• Distributed/multi-source data, hierarchical data
• No solution (binning, dimension reduction, tours) works for every situation

Interactive Graphics

• Provide additional information in response to user action
  
  
• Simultaneously show more than 2-3 variables and their relationship (multiple linked plots)
  
  
• Accommodate complex data structures
  
  

BUT…


Web-based interactive graphics may be even more size-sensitive than static graphics.

Interactive Visualization

• Lacks the rigor of a grammar of interactivity
  
  
• Design is a function of necessity (for now!), which can lead to sub-optimal graphics
  • Interactivity vs. Animation vs. Static Plots
  • Many types of interactivity, with different use cases:
    Brushing, linked plots, subsetting, zoom-and-filter
    
    
• Perceptual research is limited
  • Extremely specific use cases
  • Low-level psychological effects
  • Testing paradigms are somewhat difficult

Overall Project Goals:

• Understand historical yield increases
  100% increase in past 100 years; additional 70% increase by 2050 to meet food needs (World Bank)
  

• Associate genetic features with phenotypic traits Disease resistance, yield, nutritional content, time to maturity

• Communicate analysis results intuitively:
  • Target: Soybean farmers, plant geneticists
  • Provide full results (tables) and graphical summaries
  • Interface with existing databases and web resources

Data

• Sequencing Data (79 varieties, 75GB processed and compressed)
  
  
• Field Trials (168 varieties, 30 varieties with genetic data)
  
  
• New crosses with highest yield varieties
  (sequencing + field trials)
  
  
• Genealogy (1600 varieties)

Visualization Concerns:

• Huge number of interesting genes (70 million ID’d SNPs)
  

Visualization Concerns:

• Huge number of interesting genes (70 million ID’d SNPs)
• 79 varieties, 20 chromosomes
• Phenotype and genealogy information
• Researchers tend to work on gene subsets:
  Must be able to zoom and filter
• Optimized files for SNP results are still large (10 GB) and require significant computational resources

Visualizing SNPs

• SNP: Single Nucleotide Polymorphism, a single basepair mutation
  (A -> T, G -> A, C -> G)
• Shiny applet: Responsive applet for user-directed data subsets
• Show multiple levels of detail (less detail = lower computational load)
• Provide resources in the applet for user exploration (not just a reference tool)

Applet Design

SNP Population Distribution

Density of SNPs: Chromosome Level

Individual SNPs: Comparing Varieties

Genealogy and Phenotypes

Link

Interactive Plot Design

Good Statistical Graphics

Outline

Next Steps

• User Studies of Interactive Graphics
  • Eye Tracking
  • Click Recording
  • Content Questions
  • “At what point do humans get overloaded?”
    
    
• Color Perception for Statistical Plots
  • Colorbrewer palettes for maps
  • dichromat R package to simulate colorblindness
  • Need for validated color schemes that work well for scatterplots, bar charts, and other statistical plots
    
    
• Hierarchy of Visual Features

Goal: Understand which features are most visually important.

Goal: Understand which features are most visually important.

Other Projects

• Animint - Extends the ggplot2 implementation of the grammar of graphics to interactive plots
  
  
• USDA Soybean Population Genetics Research
  • Analysis of copy-number variants
  • Genome-wide association studies of identified SNPs
  • Genealogy database
    
    
• Data Aggregation
  • Craigslist ads
  • OkCupid
  • Location-based energy prices

Summary

• Visualization research is inherently interdisciplinary
• Graphics are evolving with new data
• Need to quantify perception to better evaluate graphs

Acknowledgements

Computation

• dplyr/plyr
• reshape2/tidyr
• CN.MOPS: CNV identification in populations of genetic data

Acknowledgements

Visualization Software

• ggplot2
• Animint
  d3 interactive web graphics using ggplot2 syntax in R
• Shiny (RStudio) interactive web applets
• Reveal.js (slides) with Rmarkdown and knitr

Acknowledgements

People

• Heike Hofmann
• Di Cook
• Michelle Graham
• Lindsay Rutter

Visual Reasoning

Graphics research often uses the lineup protocol, a hypothesis test analogue for static graphics. Goal: Understand correlation between graphical perception, lineup performance, mathematical reasoning, and classification skill.

Visual Reasoning

Conclusion: Lineups are an inductive classification task using graphics; performance is not seriously impacted by spatial ability (outside of general aptitude).

Graphical Features

Goal: Understand which features are most visually important.

Graphical Features

Goal: Understand which features are most visually important.